"Spoooooooky" Russian rational expressions 11

Algebra Level pending

\[ \mathscr{E} = 1- \left( \dfrac{2}{a-2} - \dfrac{2}{a+2} \right) \left( a-\dfrac{3a+2}{4} \right) \]

Let \( a = 2016 \). If \( \mathscr{E} \) can be expressed in the form \( \dfrac{x}{y} \), where \(x\) and \(y\) are coprime positive integers, find \(x+y\).


Credit: My former Trig teacher's worksheet of Russian rational expressions
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